
where \(w\)  denotes additive white Gaussian noise (AWGN),
and \(x_1\)  and \(x_2\)  are both repetitively group-sparse signals with
periods \(T_1\)  and \(T_2\)  respectively.
Note that here the repetitively group-sparse signal means the useful features (group-sparse) appear repetitively.
In other words, the features have group-sparse property and appear repetitively.
To avoid confusion, here the “period" is referred to as the cycle for cyclostationary signal in Ref. [1]}.
In the case of compound faults detection of bearings, useful features \(x_1\)  and \(x_2\)  also satisfy the following two conditions.
